Alfonso García Pérez

On Robustness for Hypotheses Testing

Summary A way to deal with robustness in hypotheses testing using a tail-ordering on distributions is described. We prove, under mild conditions that to test H,: 0 0ot, at level a < 0.5, the uniformly most powerful (UMP) test that accepts Ho when X has distribution function F(X ,,- F) would also accept this with X A- G if F<, G. Likewise, the UMP test that rejects HI with X - F would also reject it with X - D if D <, F, where <, is the tail-ordering defined by Loh (1984), and where F, G and D belong to the class of distributions J* defined below. For distributions of this class we define the r-value as a measure of test robustness against changes in the model distribution. We also make an analysis of test robustness using the asymptotic distribution of the random variable p-value.

Nonparametric estimation: the survival function

ResumenSe considera la función de supervivencia desconociaS(t) de una variable aleatoriaT≥0. Primero estudiamos las propiedades deS(t) y luego, la estimamos desde un punto de vista Bayesiano, obteniendo, bajo pérdida cuadrática, el estimadorn

Estadística aplicada: conceptos básicos

hat S(t) = [1 - p_n (t)]S_n (t) + p_n (t)S_0 (t)

t-Tests with Models Close to the Normal Distribution

n y el riesgo Bayes mínimo asociado dondeSn(t) es la función de supervivencia empírica,S0(t) la función de supervivencia a priori,Rmin(0)=V(S(t)) el riesgo en el problema sin muestra yn

Principios de inferencia estadística

p_n (t) = frac{{S_0 (t) - E[S^2 (t)]}}{{S_0 (t) + (n - 1)E[S^2 (t)] - nS_0^2 (t)}}, 0 leqslant p_n (t) leqslant 1

Problemas resueltos de estadística básica

n siendoŜ(t)c.s.→S(t) y Rmin(n)n→∞→0. Comparamos dicho estimador con la media a posteriori y después de ver condiciones generales bajo las cuales los coeficientes, en las estimaciones Bayesianas lineales, suman uno, terminamos dando reglas Bayes para las funciones lineales deS(t).SummaryThe unknown survival functionS(t) of a random variableT≥0 is considered. First we study the properties ofS(t) and then, we estimate it from a Bayesian point of view. We compare the estimator with the posterior mean and we finish giving Bayes rules for linear functions ofS(t).